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內容簡介

《群與對稱》講述瞭 numbers measure size， groups measure symmetry. the first statement comes as no surprise； after all， that is what numbers are for. the second will be exploited here in an attempt to introduce the vocabulary and some of the highlights of elementary group theory.
a word about content and style seems appropriate. in this volume， the emphasis is on examples throughout， with a weighting towards the symmetry groups of solids and patterns. almost all the topics have been chosen so as to show groups in their most natural role， acting on （or permuting） the members ora set， whether it be the diagonals of a cube， the edges of a tree， or even some collection of subgroups of the given group. the material is divided into twenty-eight short chapters， each of which introduces a new result or idea.a glance at the contents will show that most of the mainstays of a first course arc here. the theorems of lagrange， cauchy， and sylow all have a chapter to themselves， as do the classifcation of finitely generated abelian groups， the enumeration of the finite rotation groups and the plane crystallographic groups， and the nielsen-schreier theorem.

目錄

preface
chapter 1 symmetries of the tetrahedron
chapter 2 axioms
chapter 3 numbers
chapter 4 dihedral groups
chapter 5 subgroups and generators
chapter 6 permutations
chapter 7 isomorphisms
chapter 8 plato‘s solids and cayley’s theorem
chapter 9 matrix groups
chapter 10 products
chapter 11 lagrange‘s theorem
chapter 12 partitions
chapter 13 cauehy’s theorem
chapter 14 coujugacy
chapter 15 quotient groups
chapter 16 homomorphisms
chapter 17 actions， orbits， and stabilizers
chapter 18 counting orbits
chapter 19 finite rotation groups
chapter 20 the sylow theorems
chapter 21 finitely generated abelian groups
chapter 22 row and column operations
chapter 23 automorphisms
chapter 24 the euclidean group
chapter 25 lattices and point groups
chapter 26 wallpaper patterns
chapter 27 free groups and presentations
chapter 28 trees and the nielsen-schreier theorem
bibliography
index

前言/序言

群與對稱 [Groups and Symmetry] 下載 mobi epub pdf txt 電子書

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（3）左右對稱：或稱兩側對稱，是僅通過一個平麵（正中矢麵）將身體分為互相顯鏡像關係的兩個部分（例如脊椎動物的外形）。在正中矢麵內由身體前端至後端的軸稱為頭尾軸或縱軸，這個軸與身體長軸大都一緻。在正中矢麵內與頭尾軸成直角並通過背腹的軸為背腹軸或矢狀軸。還有與正中矢麵成直角的軸稱正中側麵軸（或內外軸）、該軸夾著正中矢麵，彼此相等且具有方嚮相反的極性，如果將兩側的正中側麵軸閤起來看成為一軸時，則稱為橫軸。在輻射對稱中，如相當於海星的一根足的同型部分，稱為副節（paramere），副節其本身成兩側對稱。一般兩側對稱的每一半為與同一軸相關而極嚮相反的同型部分，此稱為對節或體輻。副節、對節等的同型部分，一般來看，僅相互方嚮不同，可認為這是與對外界的關係相同有著密切的聯係。所以在個體發生或係統發生過程中其生活方式變化時，而與之相關的對

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（2）雙輻射對稱：隻有兩個輻射軸，彼此互成直角，形式上可以把它看成是從輻射對稱嚮左右對稱的過渡型（例如櫛水母）；

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